Jewellery and Dark Chocolate: A Mathematical Exploration
In this homework, we will delve into the world of jewellery and dark chocolate, using mathematics to better understand these fascinating subjects.
1. Counting Items in Jewellery
- Consider a collection of jewellery that includes necklaces, bracelets, and earrings.
- If you have 5 necklaces, 3 bracelets, and 4 pairs of earrings, how many different combinations can you wear?
- Use the formula: Total Combinations = Necklaces x Bracelets x Earrings.
2. Dark Chocolate: Nutritional Values
- Dark chocolate is often measured in grams.
- If a dark chocolate bar weighs 100 grams and contains 70% cocoa, how many grams of cocoa are in the bar?
- Calculate the amount of sugar if the bar contains 30 grams of sugar.
3. Color Theory and Dark Colors
- Dark colors absorb more light. If you have a palette of 5 dark colors, how many combinations of 2 colors can you create for a design?
- Use the combination formula: C(n, k) = n! / [k!(n-k)!], where n is the total number of colors and k is the number of colors chosen.
4. Dark Sunglasses and Their Impact
- If a pair of dark sunglasses costs $50 and you buy 3 pairs, what is the total cost?
- Additionally, consider the percentage discount if the store offers a 20% discount on your total purchase.
5. Summary and Reflection
- Reflect on how mathematics plays a vital role in everyday items like jewellery and dark chocolate.
- Consider the importance of calculations in budgeting and design.
By exploring these concepts, you can see how math connects with our daily lives, from fashion to food!